Calculating the Inverse Matrix After Some Elements in the Matrix Change

Key Points

• The aim is to present a new formula and algorithm for efficiently calculating matrix inverses after element perturbations.
• Proposed a computational formula for matrix inverse calculation upon perturbation of two elements.
• Developed a fast algorithm for retrieving specific elements in an inverse matrix.
• Demonstrated the algorithms with numerical examples.
• The new formula efficiently calculates the inverse after two elements change.
• The algorithm allows for quick computation of individual elements in the inverse matrix.
• Numerical examples support the practical feasibility of the proposed methods.

Abstract